If you look strictly at the numbers, there is a "right" way to pay off debt.
Mathematically, the best way to maximize your money is to focus on paying down debts with the highest interest rates first. Following that logic, if you have a $1,000 credit card bill with a 24 percent interest rate, you should tackle that before your $7,000 student loan with a 6.5 percent interest rate.
Known as the "avalanche method," this strategy minimizes the amount of interest you're paying overall, which can save you thousands over time, depending on the level of debt you have.
However, the avalanche method isn't always the most effective one because for many people it doesn't generate the motivation needed to make debt elimination a priority. In fact, researchers for the Harvard Business Review found that the opposite approach, known as the snowball method, actually proved to be the most effective strategy.
Popularized by "The Total Money Makeover " author Dave Ramsey, the snowball method prioritizes your smallest debts first, regardless of interest rate.
To try it, start by listing out all of your debts, smallest to largest. Pay the minimum balance on each one, except the smallest. For that one, dedicate as much cash as possible each month until it is repaid. Then move on to the second-smallest debt.
The idea is that you'll gain momentum by watching debts disappear, as you would watching a snowball grow bigger and bigger, and that will motivate you to continue.
"Focusing on paying down the account with the smallest balance tends to have the most powerful effect on people's sense of progress — and therefore their motivation to continue paying down their debts," Remi Trudel, one of the researchers, writes for HBR.
Ramsey likens this sense of accomplishment to going on a diet. If you begin to lose weight the first week, you'll be motivated to continue. But if you watch what you eat for weeks with no measurable progress, it becomes tempting to give up altogether.
"You need quick wins to get fired up," he writes in "The Total Money Makeover. " "When you start the debt snowball and in the first few days pay off a couple of little debts, trust me, it lights your fire."
In addition to organizing and paying off your bills in a certain order, Ramsey says the most important factor that makes the debt snowball work is focused intensity. "This means saying to yourself (and meaning it), 'To the exclusion of virtually everything else, I'm getting out of debt!'"
If you truly want to be debt-free, don't worry about concentrating too hard on the numbers if that isn't going to get you to buckle down. Ask yourself what will inspire you to keep going, no matter what.
"I have learned that the math does need to work, but sometimes motivation is more important than math," Ramsey says.
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